np.trapz 生动的解释

刺骨的言语ヽ痛彻心扉 2022-10-04 12:56 99阅读 0赞

先画坐标系，给的点围成的梯形的面积。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDMzODcwNQ_size_16_color_FFFFFF_t_70][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDMzODcwNQ_size_16_color_FFFFFF_t_70 1][]

trapz的代码：

import numpy as np
    
    
    def trapz(y, x=None, dx=1.0, axis=-1):
        """
        y : array_like
            Input array to integrate.
        x : array_like, optional
            The sample points corresponding to the `y` values. If `x` is None,
            the sample points are assumed to be evenly spaced `dx` apart. The
            default is None.
        dx : scalar, optional
            The spacing between sample points when `x` is None. The default is 1.
        axis : int, optional
            The axis along which to integrate.
        Returns
        -------
        trapz : float
            Definite integral as approximated by trapezoidal rule.
        See Also
        --------
        sum, cumsum
        Notes
        -----
        Image [2]_ illustrates trapezoidal rule -- y-axis locations of points
        will be taken from `y` array, by default x-axis distances between
        points will be 1.0, alternatively they can be provided with `x` array
        or with `dx` scalar.  Return value will be equal to combined area under
        the red lines.
        References
        ----------
        .. [1] Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule
        .. [2] Illustration image:
               https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png
        Examples
        --------
        >>> np.trapz([1,2,3])
        4.0
        >>> np.trapz([1,2,3], x=[4,6,8])
        8.0
        >>> np.trapz([1,2,3], dx=2)
        8.0
        >>> a = np.arange(6).reshape(2, 3)
        >>> a
        array([[0, 1, 2],
               [3, 4, 5]])
        >>> np.trapz(a, axis=0)
        array([1.5, 2.5, 3.5])
        >>> np.trapz(a, axis=1)
        array([2.,  8.])
        """
        y = np.asarray(y)
        if x is None:
            d = dx
        else:
            x = np.asarray(x)
            if x.ndim == 1:
                d = np.diff(x)
                # reshape to correct shape
                shape = [1]*y.ndim
                shape[axis] = d.shape[0]
                d = d.reshape(shape)
            else:
                d = np.diff(x, axis=axis)
        nd = y.ndim
        slice1 = [slice(None)]*nd
        slice2 = [slice(None)]*nd
        slice1[axis] = slice(1, None)
        slice2[axis] = slice(None, -1)
        try:
            ret = (d * (y[tuple(slice1)] + y[tuple(slice2)]) / 2.0).sum(axis)
        except ValueError:
            # Operations didn't work, cast to ndarray
            d = np.asarray(d)
            y = np.asarray(y)
            ret = np.add.reduce(d * (y[tuple(slice1)]+y[tuple(slice2)])/2.0, axis)
        return ret
    
    if __name__ == '__main__':
    
        # np.diff()
    
        res=trapz([1, 1, 2])
        print(res)

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDMzODcwNQ_size_16_color_FFFFFF_t_70]: /images/20221004/232fe58209604510a02a0aa63f89a186.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDMzODcwNQ_size_16_color_FFFFFF_t_70 1]: /images/20221004/630b8b4399cf48888c58f71ab455bbaf.png